CHƯƠNG 3_qui hoach thuc nghiem

8/8/2019 CHNG 3_qui hoach thuc nghiem

1/23

CHNG III

MT S PHNG PHPQUI HOCH THC NGHIM


2/23

3.1. Thc nghim yu t ton phn:- Nhng thc nghim m mi t hp cacc mc ca cc yu t u c thc

nghim nghin cu gi l thc nghim yut ton phn (TYT).

- C k yu t, mi yu t c n mc s th

nghim phi thc hin l:N = nk

CHNG IIIMT S PHNG PHP QUI HOCH THC NGHIM


3/23

- Nu cc th nghim ch thc hin haimc th N = 2k, hai mc gi tr bin cayu t c kho st.

- Nu chn th nghim c mt tm ixng ta c phng n cu trc c tm.

- Xt yu t c k hiu l Zj ta c:

j = 1 z k


2

minmax

jjo

j

ZZZ

!


4/23

- mc cao- mc thp

- mc c s (tm ca phng n)

Bin thin ca yu t Zj tnh t mc c s:, j = 1 z k

- Tin cho tnh ton ta chuyn sang h trckhng th nguyn nh chn tm ca min l

gc h trc ta .

, j = 1 z k


max

jZmin

jZ

o

jZ

2

max

jj

j

ZZZ

!(

j

o

jj

jZ

ZZX

(

!


5/23

- T ta c mc trn l +1, mc di l-1 tm trng vi gc ta

V d:

Nghin cu tc phn ng ha hc ca

mt phn ng cho ph thuc vo, nhit nng C, p sut P.



6/23

* Xc lp ma trn thc nghim:Cc bin c lp c chn l:

- Nhit Z1 mc cao: 300oC mc thp 200oC

- Nng Z2 mc cao: 45 g/l mc thp 35 g/l

- p sut Z3 mc cao: 1,25 at mc thp 0,75 at



7/23

Phng n th nghim c vit didng ma trn (TYT) 2 mc th nghim, sbin c lp k = 3. S th nghim th cthc hin l:

N = 23 = 8

Phng n th nghim v kt qu thnghim c trnh by trn bng 1



8/23

MA TRN TYT 23 = 8


S thnghim

Bin thc Bin m ha Kt qu

Z1 Z2 Z3 X1 X2 X3 Y

1 300 45 1,25 + + + 296

2 200 35 1,25 - - + 1223 300 35 1,25 + - + 239

4 200 45 1,25 - + + 586

5 300 45 0,75 + + - 2326 200 35 0,75 - - - 292

7 300 35 0,75 + - - 339

8 200 45 0,75 - + - 383


9/23

thun tin cho nghin cu ngi ta hm bin o xo, x

o= 1

Ma trn qui hoch vi bin o TYT 23


S thnghim X0 X1 X2 X3 Y

1 + + + + Y12 + - - + Y23 + + - + Y34 + - + + Y4

5 + + + - Y56 + - - - Y67 + + - - Y7

8 + - + - Y8


10/23

Ma trn qui hoch m bo tnh trc giao.

V

* Xc lp phng trnh hi qui

Nu dng phng trnh hi qui tuyn tnh di dng:


kjujuxxN

i

jiui z!{!!

0,,,0.1

0;1;01

{z!!!

jkjxi

ji

3322110

^

xbxbxbbY !


11/23

Theo phng php tnh h s trong phng trnh hi qui:

Ma trn XTX c dng:


YXXX

b

b

b

b

BTT

o

1

3

2

1).( !!

!

!

i i i i

iiiiioii

i i i i

iiiiioii

i i iii iiioii

i i i

ioiioiioi

i

oi

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

C

2

323133

32

2

2122

3

12

1

2

11

8

1

321

2


12/23

T tnh cht trn ta c:


81000

08

100

008

10

0008

1

)(;

80000800

0080

0002

1 !! XXXX TT

!

ii

ii

ii

i

ioi

T

yx

yx

yx

yx

XX

3

2

1


13/23

Suy ra:

Tnh

b1 = 34,625, tng t ta c:

b2 = 63,125, b3 = -0,375, bo = 311, 125


!!!

ii

ii

ii

i

ioi

TT

o

yx

yx

yx

yx

YXXX

b

b

b

b

B

3

2

11

3

2

1

81000

08

100

008

10

00081

.)(

!

!N

i

ijij yxN

b1

1

8

8

1

1

1

!

!i

ii yx

b

8

383.1339.1292.1232.1586.1239.1122.1296.11

!b


14/23

Ta c m hnh: Y = 311,125 + 34,625x1 + 63,125x2 0,375x3

xt m hnh y hn

Ma trn qui hoch c m rng


3223311321123322110

^

xxbxxbxxbxbxbxbbY !

S thnghim X0 X1 X2 X3 X1X2 X1X3 X2X3 Y

1 + + + + + + + 296 331,125 1233,765

2 + - - + + - - 122 139,875 319,515

3 + + - + - + - 239 221,875 293,265

4 + - + + - - + 586 551,625 1181,640

5 + + + - + - - 232 196,875 1230,7656 + - - - + + + 292 274,125 319,515

7 + + - - - - + 339 356,125 293,265

8 + - + - - + - 383 417,375 1185,640

^

Y2

^

)( iYY


15/23

Cc hiu ng tng tc c xc nh tng t nhhiu ng tuyn tnh.

thay s vo

Tng t: b13 = - 8,625, b13 = 67,125

Phng trnh hi qui lc ny c dng

Y = 311,125 + 34,625x1 + 63,125x2 0,375x3 75,625x1x2 = 8,625x1x3 + 67,125x2x3


N

Yxx

b

N

i

iilj

jl

!

!1

)(

N

Yxx

b

N

i

ii!! 1

21

12

)(

625,758

838.1339.1292.1232.1586.1239.1122.1296.1(12 !

!b


16/23

*Kim nh tnh ngha ca cc h s phng trnh hi qui

- V ma trn (XTX)-1 l ma trn ng cho nncc h s c lp vi nhau.

- Loi b cc h s khng c ngha khng nh

hng n h s cn li.- Cc h s kim nh theo tiu chun Student (t).

- Mi h s ca phng trnh c xc nh vi

chnh xc.


N

ss thbj !


17/23

- Khng lm th nghim song song xc nh phngsai ti hin sth ta lm 3 th nghim tm phng n tanhn 3 gi tr.


S thnghim

Bin thc Bin m ha Kt qu

X1 X2 X3 Y0

1 250 40 1 0 0 0 295

2 250 40 1 0 0 0 312

3 250 40 1 0 0 0 293

0

1Z0

2Z

0

3Z


18/23


3003

293312295

3

3

1

4

!

!! o

o

y

Y

109

13

3

1

2

4

2!

!

oo

th

yy

s

440,10109 !!ths

69,38

440,10!!!

N

ss thtj


19/23

ngha ca cc h s c kim nh theo tiu chunStudent t

Ta tnh c:

t1 = 9,38, t2 = 17,107, t3 = 0,1016, t12 = 20,494

t13 = 2,337 t23 = 18,191


jb

j

j

s

bt

||!

315,8469,3

125,311!!ot


20/23

Tra bng tp(f) vi p = 0,05, f = 2f = l- 1 bc t do ti hin

ls th nghim song song tm

t0,05 (2) = 4,3V t3 < tp(f), t13 < tp(f)Cc h s b3, b13 b loi phng trnh lc ny cdng:


322121

^

125,67625,75125,63625,34125,311 xxxxxxY !


21/23

* Kim nh s tng thch ca phng trnh hi qui:S tng tch ca phng trnh hi qui c kim nhbng tiu chun Fisher.

Trong :

N s th nghim

l- s th nghim tm


2

2

th

du

s

s

F !

lN

yy

s

N

i

ii

du

!

!1

2^

2

)(


22/23

Thay s

Tra bng F1-p (f1, f2) vi p = 0,05 f1 = 3, f2 = 2

f1 bc t do phng sai tng thch

f1 = N l

N s th nghim : 8

l h s c ngha trong phng trnh hi qui: 5


791,20183

3742,60562!!dus

521,18109

79

1,2

0182

2

!!!th

du

s

s


23/23

f2 bc t do phng sai ti hin

f2 = N - 1

N s th nghim song song tmF0,05 (3,2) = 19,2

phng trnh hi qui tng thchvi thc nghim.


),(1 21 ffpFF

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